Want to prove Var(xy)=E[x]^2*var(y)+E[y]^2*var(x)+var(x)*var(y)

yabi

New member
Want to prove Var(xy)=E[x]^2*var(y)+E[y]^2*var(x)+var(x)*var(y)

I want to prove above-mentioned formula using following formula:
Var(y)=Ex[var(y/x)]+varx[E(y/x)]

In next step I want to prove the title-mentioned formula using Taylor series expansion.

Will be happy if someone could give a hint on how can I prove this formula.

Last edited by a moderator:

Subhotosh Khan

Super Moderator
Staff member
I want to prove above-mentioned formula using following formula:
Var(y)=Ex[var(y/x)]+varx[E(y/x)]

In next step I want to prove the title-mentioned formula using Taylor series expansion.
Can you provide mathematical equations to describe E(x) and var(x)

Please show us what you have tried and exactly where you are stuck.

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